Multibody System Dynamics

, Volume 42, Issue 3, pp 317–345 | Cite as

A unified formulation for mechanical joints with and without clearances/bushings and/or stops in the framework of multibody systems



Virtually all machines and mechanisms use mechanical joints that are not perfect from the kinematic point of view and for which tolerances, in the fitting of their components, are specified. Together with such controlled clearances, mechanical joints may require the use of bushing elements, such as those used in vehicle suspensions. Furthermore, in many situations the joints exhibit limits (stops) in their translational or rotational motion that have to be taken into account when modeling them. The dynamic response of the mechanical systems that use such realistic mechanical joints is largely dependent on their characteristic dimensions and material properties of the compliant elements, implying that correct models of these systems must include realistic models of the bushing/clearance joints and of the joint stops. Several works addressed the modeling of imperfect joints to account for the existence of clearances and bushings, generally independently of the formulation of the perfect kinematic joints. This work proposes a formulation in which both perfect and clearance/bushing joints share the same kinematic information making their modeling data similar and enabling their easy permutation in the context of multibody systems modeling. The proposed methodology is suitable for the most common mechanical joints and easily extended to many other joint types benefiting the exploration of a wide number of modeling applications, including the representation of cut-joints required for some formulations in multibody dynamics. The formulation presented in this work is applied to several demonstrative examples of spatial mechanisms to show the need to consider the type of imperfect joints and/or joints with stops modeling in practical applications.


Kinematic joints Clearance joints Bushing joints Constraint violation Joint stops Numerical efficiency 



This work was supported by FCT, through IDMEC, under LAETA, project UID/EMS/ 50022/2013.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.IDMEC, Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal
  2. 2.School of Energy, Geoscience, Infrastructure & SocietyHeriot-Watt UniversityEdinburghUK

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